30.54cm is the length of the vertical leg.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In a right angled triangle the horizontal leg has a measure of 42.7 centimeters(cm).
The hypotenuse has a measure of 52.5cm.
We need to find the measure of the vertical leg.
We can find this by using pythagoras theorem.
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
52.5²=42.7²+x²
2756.25=1823.29+x²
Subtract 1823.29 on both sides
2756.25-1823.29=x²
932.96=x²
Taking square root on both sides
x=30.54
Hence, the length of the vertical leg is 30.54cm.
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Since 1992, the value of homes in a neighborhood has doubled every 16 years. The
value of one home in the neighborhood was $136,500 in 1992.
a. What is the value of this home, in dollars, in the year 2000? Explain your
reasoning.
b. Write an equation that represents the growth in housing value as a function of
time in t years since 1992.
c. Write an equation that represents the growth in housing value as a function of
time in d decades since 1992.
d. Use one of your equations to find the value of the home, in dollars, 1.5 decades
after 1992.
a. To find the value of the home in the year 2000, we need to find how many 16-year intervals have passed between 1992 and 2000. Since 2000 is 8 years after 1992, we have that $\frac{8}{16} = \frac{1}{2}$ 16-year intervals have passed. This means that the value of the home has doubled once since 1992, so it is now worth $136,500 * 2 = $273,000.
b. The growth in housing value as a function of time in t years since 1992 can be represented by the equation $V(t) = 136,500 * 2^{\frac{t}{16}}$, where $V(t)$ is the value of the home in t years after 1992 and 2 is the factor by which the value has doubled every 16 years.
c. The growth in housing value as a function of time in d decades since 1992 can be represented by the equation $V(d) = 136,500 * 2^{\frac{d * 10}{16}}$, where $V(d)$ is the value of the home in d decades after 1992 and 2 is the factor by which the value has doubled every 16 years.
d. To find the value of the home 1.5 decades after 1992, we can use the equation $V(d) = 136,500 * 2^{\frac{d * 10}{16}}$. Plugging in $d = 1.5$, we get $V(1.5) = 136,500 * 2^{\frac{1.5 * 10}{16}} = 136,500 * 2^{0.9375} = $351,284.375.
How much is 50 km in hours?
The mentioned data of 50 kilometres in hours is speed of 50 kilometres per hour.
The 50 kilometres refere to the distance and hour is representative of time. Now, ratio of distance and time indicates the speed or rate of movement of the concerned thing.
The speed or rate of movement holds significance in real world calculations. Based on it, the speed of bucket carrying water from well can be increased or decreased, movement of vehicles which may cause accident, distance covered by trains, airplanes, ships and other transport objects by specific speed in particular time limit.
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PLEASE HELP WITH THIS GEOMETRY!!!!! 50 POINTS & BRAINLIEST
Answer:
angle L= 55 degrees
Angle Lmk= 62 degrees
Step-by-step explanation:
we will find Lmk first by subtracting 118 by 180
180-118
62
Now the sum of all the three angles of any triangle equal 180
so we can set all these angles equal to find x
(6x-9)+(4x+7)+62=180
10x-2+62=180
10x+60=180
-60. -60
10x=120
/10. /10
x=12
4(12)+7
48+7
55
Hopes this helps have a wonderful day
Please help asap. Anything helps!!!
Answer: 2x
Step-by-step explanation:
please answer question 10
Answer: A song costs 0.99$, and an album 9.99$
Step-by-step explanation:
14.94=5x+1y
22.95=3x+2y
29.88=10x+2y
22.95=3x+2y
subtract
6.93=7x
x=0.99$
y=9.99
Find the slope of the line passing through the points (8, 4) and (8, -9).
slope:
Find the slope of the line passing through the points (-7, 5) and (5, 5).
slope:
Answer:
Step-by-step explanation:
Slope is "rise over run" or change is y values divided by change in x values
the change is x values is zero. 8-8=0. Anything divided by zero is infinity.
the slope is infinite. The line connecting the 2 points is a vertical line, x=8.
Vertical lines have infinite slope.
> Solve the problem.
David paints a set for a
play. The table shows the
proportional relationship
between gallons of paint
and the area of the set.
What area of the set can
11 gallons of paint cover?
Paint (gal) Area (sq ft)
y
X
400
640
1200
2.5
4
7.5
11
1760 ft² area will be covered with 11 gallons of paint.
What is proportionality?When two quantities are related in a linear relationship, then that arrangement is said to be in proportion.
Given that, a proportional relationship between gallons of paint and the area of the set.
The relation is :-
x (gallon of pain) y (area)
2.5 400
4 640
7.5 1200
11 ?
Establishing the proportion,
Area covered in 1 gallon =
400/2.5 = 640/4 = 1200/7.5 = 160 ft²
That means, in 1 gallon, there will be 160 ft² area covered.
Therefore, in 11 gallons = 160×11 = 1760 ft²
Hence, in 11 gallons, 1760 ft² area is being covered.
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The diameter of the hubcap of a tire is 46 cm find the area in square centimeters of this hubcap write your answer in the terms of pi 
Answer:
[tex]529\pi[/tex] cm²
Step-by-step explanation:
[tex]d=46 \implies r=23 \\ \\ A=\pi r^2=\pi (23^2)=529\pi[/tex]
i need help with my Math homework please
Answer:
Step-by-step explanation:
15% of 3,000 is 450
Find the slope of the line that passes through (5, 8) and (2, 4).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
4/3
Step-by-step explanation:
4-8/2-5
-4/-3
4/3
hopes this helps
Answer: 4/3 is the slope
In circle L with m/KLM = 60°, find the angle measure of minor arc KM.
Answer:
minor arc KM = 60°
Step-by-step explanation:
the measure of an arc is equal to the measure of the central angle that subtends it , then
arc KM = ∠ KLM = 60°
how much time is required for a 5.75 mgmg sample of 51cr51cr to decay to 0.700 mgmg if it has a half-life of 27.8 days? express the time in days to one decimal place.
The time is required for a 5.75 mg sample of 51cr to decay to 0.700 mg is 99.4 days
What is decay constant?
A property of unstable radionuclides that spontaneously decay at various rates to a more stable atomic configuration is the radioactive decay constant (λ); The higher the decay constant, the faster the parent radionuclide depletes over time.Decay constant k = ln(2) / half life
= ln(2) / 27.8
= 0.024933 day⁻¹
For first order decay:
ln(M / M₀) = -kt
where M is mass remaining at time t and M₀ is initial mass.
ln(0.700/5/75) = -0.024933 * t
Time, t = 99.4 days
Hence, time is required for a 5.75 mg sample of 51cr to decay to 0.700 mg is 99.4 days.
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What is the equation for the line in slope-intercept form? enter your answer in the box.
The equation for the line in slope-intercept form y=-4x+5
1. We will, first of all, Determine the slope by counting down and over from one place to another. Let's start at (-2,13) and work our way down (0,5)
If at all you are concerned about miscounting, you can use the slope formula, which is y2-y1/x2-x1.
5-13/0--2 \s = -8/2
The gradient is -4.
2. Determine where the line intersects the y-axis to obtain the y-intercept. It crosses it at 5 here.
3. Write the equation in slope-intercept form, y=mx+b, where mx is the slope and b is the y-intercept.
y=-4x+5
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Consider the inequalities -2r<10 and -6<-2x
The value of the variable 'x' is less than 3 and the value of the variable 'r' is greater than negative 5.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequalities are given below.
-2r < 10 and -6 < -2x
The value of the variable 'r' is given as,
-2r < 10
2r > -10
r > - 10/2
r > - 5
The value of the variable 'x' is given as,
-6 < -2x
2x < 6
x < 6 / 2
x < 3
The value of the variable 'x' is less than 3 and the value of the variable 'r' is greater than negative 5.
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-(7x-8)=2-5x please I need help
Answer:
x = 3.
Step-by-step explanation:
To solve this equation, we first need to get all the terms containing the variable x on one side of the equation and all the constants on the other side. We can do this by adding 8 to both sides of the equation. This will give us:
$$-(7x-8) + 8 = 2-5x + 8$$
Next, we can simplify the left side of the equation by combining the two terms:
$$-7x + 8 + 8 = 2-5x + 8$$
This gives us:
$$-7x + 16 = 2-5x + 8$$
Now, we need to get all the x terms on one side and all the constants on the other side. We can do this by adding 5x to both sides of the equation:
$$-7x + 16 + 5x = 2-5x + 8 + 5x$$
This gives us:
$$-2x + 16 = 2 + 8$$
We can simplify the left side of the equation by combining the two terms:
$$-2x + 16 = 10$$
Now, we need to get all the x terms on one side and all the constants on the other side. We can do this by subtracting 16 from both sides of the equation:
$$-2x + 16 - 16 = 10 - 16$$
This gives us:
$$-2x = -6$$
To solve for x, we need to divide both sides of the equation by -2:
$$\frac{-2x}{-2} = \frac{-6}{-2}$$
This gives us:
$$x = 3$$
Therefore, the solution to the original equation is x = 3.
You rent an apartment that costs \$1600$1600 per month during the first year, but the rent is set to go up 9.5% per year. What would be the rent of the apartment during the 9th year of living in the apartment? Round to the nearest tenth (if necessary).
The rent of the apartment during the 9th year of living in the apartment is $362
What would be the rent of the apartment during the 9th year of living in the apartment?It should be noted that based on the information given, the person rent an apartment that costs $1600 per month during the first year, but the rent is set to go up 9.5% per year.
This will be:
= $1600 × (1 + 9.5%)^9
= $1600 × 1.095^9
= $1600 × 2.2632
= $3620
The rent is $3620.
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which expression represents w^-7 · w³ written in simplest form
Answer:
1/w^4
Step-by-step explanation:
Consider the vector field F(x,y,z)=⟨−7y,−7x,9z⟩. Show that F is a gradient vector field F=∇V by determining the function V which satisfies V(0,0,0)=0.V(x,y,z)=
The gradient of the vector field F(x , y , z) = ⟨−7y , −7x , 9z⟩ be
F'(x , y , z) = < 0 , 0 , 9 > i.e. F'(x , y , z) = 9k.
Given, a vector field F(x , y , z) = <-7y , -7x , 9z>.
we have to find the gradient of the vector field F = ∇V.
Also, the function V satisfies the condition V(0 , 0 , 0).
As, we know to find the gradient of the vector field F(x , y , z) we differentiate the vector field or differentiate the vector field partially.
F(x , y , z) = <-7y , -7x , 9z>
F(x , y , z) = -7yi - 7xj + 9zk
On differentiating, we get
F'(x , y , z) = <d(-7y)/dx , d(-7x)/dy , d(9z)/dz>
F'(x , y , z) = < 0 , 0 , 9 >
F'(x , y , z) = 9k
So, the gradient of the vector field F(x , y , z) be, 9k
Hence, the gradient of the vector field F(x , y , z) be
F'(x , y , z) = < 0 , 0 , 9 >
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Lisa works two jobs to pay for college. She tutors for $20 per hour and also works as a library assistant for $12 per hour. Due to her class and study schedule, Lisa is only able to work up to 18 hours per week but must earn at least $200 per week. If T represents the number of hours Lisa tutors and L represents the number of hours she works as a library assistant, which system of inequalities represents this scenario?
Answer:
20T+12L[tex]\geq[/tex]200
T+L[tex]\leq[/tex]18
Step-by-step explanation:
how many points does a team get when a player makes a shot from more than 25 feet away?
Answer:
e
Step-by-step explanation:
A senior accounting major at midsouth state university has job offers from four cpa firms. To explore the offers further, she asked a sample of recent trainees from each firm: how many months did you work before receiving a raise in salary? using the following anova table, is there a difference in the mean number of months before receiving a raise among the four firms? use the 0. 01 level of significance. Analysis of variance source df ss ms f p factor 3 25. 89 8. 63 4. 27 0. 031 error 11 22. 21 2. 02 total 14 48. 10 required: a. What are the null and alternate hypotheses? b. What is the test statistic? (round your answer to 2 decimal places. )
A) Reject H0 if F > 5.417.
B) We conclude that the average number of months before a raise was granted varied between the four CPA firms at the 0.05 level of significance but are unable to rule out the null hypothesis.
Given,
a) According to the table, the values for df1 and df2 are 3 and 15, respectively. Furthermore, a significance cutoff of = 0.01 is offered.
An additional f-value of 1.75 is given.
Given the significance level of = 0.01 and the corresponding values of df1 and df2 from the f-distribution table, we have;
F-critical 5.417
Normally, we reject H0 if F > 5.417.
We conclude that we do not rule out H0 at the 0.01 level of significance in this case because F is 1.75 5.417.
b) Using the values of df1 = 3 and df2 = 15 for 0.05 level of significance from the second linked table, we have
F-critical has a value of 3.2874.
The f-value is once more less than this significant one.
As a result, we cannot conclude that the average number of months until a raise was granted varied among the four CPA companies at the 0.05 level of significance and reject the null hypothesis.
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Please help me. Write each proof
Please help please
Can Someone Solve This By Using The Formula a^2+b^2=c^2
Answer: 72 cm
Step-by-step explanation:
78 is the hypotenuse, so that it will be the c
30^2 + b^2 = 78^2
900 + b^2 = 6084
b^2 = 5184
b= 72cm
what is the quation of the unit cirle? that is what conditoon must x and y satify if (x,y) is 1 unit form the origin
What does the bar in a fraction mean?
Answer:
A fraction bar separates the numerator and denominator of a fraction. It indicates that a division of the numerator by the denominator will be performed.
Step-by-step explanation:
In math, a fraction bar can be defined as a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions. Fraction bars or fraction strips are a part-to-whole representational model. Each part of a fraction bar represents one unit out of a whole.
Answer:To separate the top and bottom numbers.
Step-by-step explanation:In math, a fraction bar can be defined as a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions.
If you can buy 2 bags of chips for $125. How many bags of chips can you get with $9,455 dollars? $7,600?
$1,000,000? Use a Ratio, ratio table, or equation to solve.
By using $9,455 dollars we can get 151 bags of chips and $7,600 dollars we can get 122 bags of chips and 16000 bags for $1,000,000 dollars.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that you can buy 2 bags of chips for $125.
We need to find how many bags of chips we can get by $9,455 dollars,
$7,600 dollars and $1,000,000 dollars.
2/125=x/9455
Apply cross multiplication
2×9455=125x
18900=125x
Divide both sides by 125
x=151
So 151 bags we can get by using $9,455 dollars.
Now for $7,600 dollars.
2/125=x/7,600
2(7600)=125x
15200=125x
x=121.6 =122
So 122 bags we can get by using $7,600 dollars.
Now for $1,000,000
2/125=x/1,000,000
2000000=125x
Divide both sides by 125
16000=x
16000 bags for $1,000,000
Hence, 151 bags we can get by using $9,455 dollars, 122 bags we can get by using $7,600 dollars and 16000 bags for $1,000,000
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when making decisions: question 15 options: qualitative factors are the most important both quantitative and qualitative factors are unimportant appropriate weight must be given to both quantitative and qualitative factors quantitative factors are the most important
When making decisions: c) appropriate weight must be given to both quantitative and qualitative factors.
Decision-making is a difficult process, especially when the issue at hand is complex and the significance of the outcome impacts the stakeholders. Decision-making is his five-step process. Recognize situations that require decision making. identifying and developing alternative courses of action; evaluating alternatives; choosing one of the alternatives and carrying out the chosen steps.
Quantitative decisions are primarily based on statistical analysis of collected data, whereas qualitative decisions are based on many algorithms such as data type and quality, factors influencing collected data, and risk assessment. It is based on more than just numeric data values to make decisions.
Quantitative factors are the basis of numerical determination. The impact of the decision on stakeholders and their reactions. investment valuation; break-even analysis; market research; sales forecasting; critical path and decision tree analysis. Qualitative factors consider other aspects that can influence the outcome of a decision, such as a SWOT (Strength Weakness Opportunities Threats) analysis. HR management issues such as motivation, morale and retention. PEST (Political, Economic and Social Technology); Advertising and Propaganda; Long-Term Survival/Development Issues and Stakeholder Analysis.
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Find the area of a polygon with vertices A(–3, 1), B(–3, 4), C(7, 1), D(7, 4)
The area of the given polygon is 30 square units.
How to calculate the area of a triangle with coordinates of its vertices?The area of a triangle can be calculated using the formula 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)] where (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the coordinates of its vertices. This formula is also useful in finding the area of any polygon with given coordinates.
The area of the given polygon can be calculated by the expression of the area of triangle as 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)].
The given polygon can be divided into two ΔABC and ΔACD,
Then, the area is given as follows,
Area of ΔABC + Area of ΔACD
= 1/2|[-3(4 - 1) + -3(1 - 1) + 7(1 - 4)]| + 1/2|[-3(1 - 4) + 7(4 - 1) + 7(1 - 1)]|
= 1/2 × 30 + 1/2 × 30
= 30
Hence, the area of the given polygon is 30 square units.
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HELP ME!! I will give brainly
Answer:
-4
Step-by-step explanation:
First find the slope of the original line
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } \\\frac{1-0}{4-0} \\\frac{1}{4}[/tex]
Slope = 1/4
Then take it's negative reciprocal to get the slope of the perpendicular line by dividing 1 by the slope and then changing the sign
-4
find x in the equation
x = 2
x = −2
x equals 392 over 9
x equals negative 392 over 9
Answer:
x= -2
Step-by-step explanation:
5x+1/3=1/3x-9
-1/3x. -1/3x
4 2/3x+1/3= -9
-1/3. -1/3
4 2/3x= -9 1/3
14/3x= -28/3
/14/3. /14/3
x= -28/3*3/14
x= -84/42
x= -2
hopes this helps please mark brainliest
Answer:
x = -2
Step-by-step explanation:
5x + 1/3 = 1/3x - 9
5x - 1/3x + 1/3 = -9
5x * 3 15x
-- > -- (remember -> 5x is the same as 5/1x)
3 3
15x/3 - 1/3x + 1/3 = -9
14x/3 + 1/3 = -9
14x+1/3 = -9 (14x + 1 is ALL over 3)
Now multiply by 3 on both sides to cancel out the denominator since 3 is the denominator.
14x + 1 = -27
14x = -28
(divide by 14 to both sides)
x = -2